Question

Question #6dd84

Answer 1

Proved L.H.S. = R.H.S.

Explanation:

We have to prove, `(sin x cos x)/[(1+cos x)(1-cos x)] = cot x`

L.H.S. = `(sin x cos x)/[(1+cos x)(1-cos x)}`

`rArr (sinx cos x)/(1^2 - cos^2x)` { As `(a+b)(a-b) = (a^2-b^2)`]

`rArr (sin x cos x)/sin^2x` [As `sin^2x+cos^2 = 1, so, 1 - cos^2x = sin^2x`]

`rArr cos x/sin x`

`rArr cotx` = R.H.S.